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Osnat Youssin Hebrew magic: The Priest, the Scribe, (the prophet) and the woman. As seen in the Hebrew Scriptures through mathematical number theory. 1 Abstract: Perfect numbers appear in Scriptures either plainly or encrypted as gematria numerical value of the word/sentence. Why this symbolism? How could be that the gematria 1 Oil painting on cover is reproduction of “New Moon Prayer “ by O.Youssin
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Hebrew Magic

Oct 09, 2014

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Page 1: Hebrew Magic

Osnat Youssin

Hebrew magic: The Priest, the

Scribe, (the prophet) and the

woman.

As seen in the Hebrew Scriptures through

mathematical number theory.1

Abstract: Perfect numbers appear in Scriptures

either plainly or encrypted as gematria –

numerical value of the word/sentence. Why this

symbolism? How could be that the gematria

1 Oil painting on cover is reproduction of “New Moon

Prayer “ by O.Youssin

Page 2: Hebrew Magic

appears before Hellenism – as usually accepted

time for this method?

The sequence of perfect numbers can be used as decoding

sequence in Scriptures, which brings us somewhere – to the

curse of Eva, to the lost and found Torah book. Greek-Jewish

antagonism. We argue that perfect numbers in early

traditions – had double meaning of perfection and curse,

especially related to women, and that that tradition was

overcome and ceased to exist – and the curse no longer was

attributed to women – in later times.

Subject matter: Judaism, Hebrew, mathematical linguistics

Keywords: Hellenism, gematria2, perfect numbers, bible,

encryption

Other important words: life, death, perfection, beauty,

temple, Sabbath, sanctity

Hellenism, gematria, sofrim3, perfect numbers.

2 Gematria – from Greek, is the numeric value of the

world, calculated as sum of numeric values of Hebrew letters, see

Liberman “Hellenism” on use of gematria and “Tikkun sofrim” –

corrections of the scribes.

According to Wikipedia - (http://en.wikipedia.org/wiki/Gematria

)”The first attested use of gematria occurs in an inscription of

Assyrian ruler Sargon II (727–707 BCE) stating that the king built

the wall of Khorsabad 16,283 cubits long to correspond with the

numerical value of his name.”

3 Scribes, who wrote (and still write) Torah scrolls on permanent

– without vowels or musical – liturgical signs. First it was written in

Page 3: Hebrew Magic

Let’s begin by introducing a notion of perfect numbers, a

special numbers, which play important role in mathematical

Number theory. The perfect number is a number, that the

sum of its dividers is equal to it. The first perfect number is

6=1+2+3, the second 28=1+2+4+7+14, and the third 496.

The question whether there are odd perfect number

remains an open problem to this day, there are also several

other open questions concerning those numbers.4

antique “Ashurit” script, which was changed later to the Hebrew script

(see tractate Sofrim), the same script is used in Israeli modern press.

See also

4 In fact, the writer of this article does not know of any other

perfect numbers except in the form

2p-1

*(2p

-1)

Where p is a prime number and 2p

-1 is also prime, which is to

say -does not have any dividers with exception of 1 and itself. For an

introduction to elementary number theory see any introductory course.

According to the theorem of Euclid, any number can be shown

as multiplication of powers of some prime numbers in unique way, for

example 24=23 * 3, 360=2

4 * 3

2 * 5

1 , 1960=2

3 * 7

2 * 5

1

and in general X=P1q1

* P2q2

* P3q3

* …* Pnqn

Where P1, P2... Pn are prime numbers and q1,q2...qn –natural

numbers. There is a Euclid’s Algorithm for such a form, which is called

factorization. It takes long to find all prime dividers of very big integers. It

is why some forms of cryptography use factorization as an encryption

method.

It is why it will be not so unusual for the sages and sofrim(sofer

actually means “scribe”, but literally – somebody who counts, as sofer

Torah was usually counting words, letters, verses and, perhaps also

gematria, out of habit seeing letters also as numbers.

Page 4: Hebrew Magic

A few years ago there was a (mathematics) internet site,

promising 100K $ for finding a next perfect number (from some

mathematical fond), which would be really very big, millions of signs, by

using combined calculative power of computer networks and

sophisticated algorithms. So, perhaps, fascination with perfect numbers is

not so unusual for modern times also, though it is difficult for me to

understand immediate use of those numbers, rather – of algorithms to

find them, which, as is easy to see, are algorithms of quick factorization,

which, as I said, is used today in cryptography, but perhaps will be not

used in future if quantum computer will replace the common one.

Here is analytic version of generalization of perfect numbers.

Theorem

Let’s define σ(n)=Σd(d divides n, including 1 and n itself). Let’s

study function f(n)= σ(n)/n,

Obviously f(n) = 2 for perfect n.

1.prove, that f(n) is not limited when n→∞

2. prove, that f(n) is dense everywhere

3. What values f (n) takes and does not take?

Letter Number

1 א

2 ב

3 ג

4 ד

5 ה

6 ו

Page 5: Hebrew Magic

7 ז

8 ח

9 ט

10 י

20 כ

30 ל

40 מ

50 נ

60 ס

70 ע

80 פ

90 צ

100 ק

200 ר

300 ש

400 ת

500 ת"ק

600 ת"ר

700 ת"ש

800 ת"ת

Page 6: Hebrew Magic

Gematria (from Greek) is sum of numerical values of

Hebrew letters, which correspond to an order of

alphabet. Tanaim were interpreting words according to

their common gematria usually as means of

entertainment or for better remembering of things.

Gematria was known at least from time of Tanaim 70-200 CE:

Mishnah in Pirkei Avot 3:235

Rabbi Eleazar Chisma said: the laws of mixed bird offerings and the key to

the calculations of menstruation days—these, those are the body of the

“halakhah”6 . The calculation of the equinoxes and gematria are the desserts

of wisdom.

.

5 .לחכמה פרפראות וגמטריאות תקופות. הלכות גופי הן הן נדה ופתחי קנין, אומר חסמא בן אלעזר רבי

6 Jewish religious Law

900 תת"ק

1000 תת"ר

Page 7: Hebrew Magic

Perfect numbers in Jewish tradition

Perfect numbers were known, for example, to Philo from

Alexandria, the Jewish-Hellenistic philosopher from 2nd

century. In his allegorical commentary to the book of

Genesis he writes, that the 6 days of creation were not

necessarily 6 days, but is just allegory for perfection, as the

number 6 is perfect, which means - the creation is perfect.

God had celebrated the perfection by sanctifying the

seventh (Kiddush Sabbath) – plus than perfect day, as do we

in His steps.

Let's first assume that Philo is right and let's see if there is

any significance to next perfect numbers...

The next holiday (which occurs more often than others) and

the first commandment given to Israel as the newly

emerging nation, in the book of Exodus is Rosh-Hodesh, the

New Moon holiday, which happens about every 29.5 days,

Page 8: Hebrew Magic

the exact phase calculated already in tractate Rosh-

Hashanah. The New Moon is sanctified by the people of

Israel (Kiddush levana) from ancient times (Exodus).

Actually, it is considered to be the first “mitzvah” -

commandment – given to Israel (not counting 1-2

commandments in the book of Genesis) to observe the

moon and sanctify it (at the beginning of its phase). The

holiday was celebrated in ancient times in much more

festive way, with additional Temple services, one or two

days, leaving exactly 28 days of the rest of the month, which

is a perfect number.

The other cosmic event related to number 28 is “blessing of

the sun” (“Birkat haHama”), which is first mentioned in

Baraita brought in Babylonian Talmud.

Sabbath does not depend on whether Israel keeps or

sanctifies it. In contrast,

It is rather Israel who sanctifies the “astronomical” events

and objects. The sanctification is final; it does not matter

whether the accounts were precise or wrong. So many

consider the blessing of the sun be a rather symbolic event,

which gives an opportunity to bless it.

As in IQ test, we can try to find the allegory of perfect

number as we understand it in Modern Judaism (some

people could try it in Christianity).

Is there any holiday associated with number 496 (next

perfect number) or 497? As Jewish holidays are based on

lunar-sun cycles and 365.25 (number of days in the year) is

Page 9: Hebrew Magic

far from 496, it seems, there was no such holiday. 7 So, let's

see, when else there is sanctifying (K D SH)? In modern

Judaism the next best guess is – marriage, to be precise – a

woman is “sanctified” (meKuDeShet).

The New Moon prayer, which is recited by men alone,

resembles – in some aspects, of course - the sanctifying of

woman, as the Moon is obviously feminine, her period is

exactly this as woman’s and the men promise to avoid

touching it and sanctify her exactly as if it was a woman.

There is no “sanctifying” in the blessing of the sun;

“haHama” obviously is associated with the masculine.

Marring a woman involves the act of sanctifying also, but it

is not usually associated with any perfect number. Sabbath

could also be considered feminine, the ‘bride’, though this

association appears much later with the kabalistic nuances.

496

As the next perfect number 496 is not easily found in Bible,

we can try Jewish numerical methods to find uses of it. For

example – gematria 8

7 There is in fact 497=“HaSUKOT” and “SUKOTA” (first

station of Israel in the desert after exodus from Egypt), in full

spelling, but it does not appear in (menukad) vocalized text,

instead it appears in full text in Exodus 12:37: And children of

Israel moved from Raamses to Sukkoth, about 6 hundred

thousand legs of men, not counting children.

רגלי אלף מאות-כשש, סוכותה, מרעמסס ישראל-בני ויסעו

מטף לבד, הגברים .

8 If you by accident have Bar-Ilan University’ “שו"תים”

Page 10: Hebrew Magic

The first time the gematria of a word equals 496=24 * ( 25 -

1) -first big enough perfect number encoded as gematria, is

the word “VeYaFT” in the phrase “ אלוהים ליפת וישכן 9ויפת

God enlarge Japheth, and he shall dwell in the“ ”"באוהלי שם

tents of Shem ““ (Genesis 9,27). 10,2 The sons of Japheth:

Gomer, and Magog, and Madai, and Javan…(Greece)

This verse is usually understood as saying that the Greek

Sciences are used – can find their place - in the religion of

Jews. So it would be perhaps no wonder, if the Bible was

using perfect numbers, or number theory, known to already

to a Greek Euclid about 600 B.C.E.

The verse can also serve as a reminder, that gematria

appeared as Hellenism in Hellenistic period. If the gematria

was not meant when the Torah was written, the words with

gematria 496, if any, would be random – would have

random meaning.

In the theme of Abraham's trial in sacrifice of Isaac in

Genesis , we see that המאכלת - “HaMAKeLeT”- the knife

for sacrifice, used here as testing instrument of innocence of

Isaac (according to modern Hasidic interpretation) in the

life-death justice, have gematria of 496.

Genesis 22:6-11

9 Actually the word translates as ‘and (he, she, you, I, we, they)

(worked, made, did) beautifully’ which could be understand as a Torah

encouraging answer to a researcher – “you do nice”, because the word

was find with the aid of the software, which hence could be seen as an

Artificial Intelligence program, communicating with the researcher

personally.

Page 11: Hebrew Magic

6 And Abraham took the wood of the burnt-offering, and

laid it upon Isaac his son; and he took in his hand the fire

and the knife; and they went both of them together. 7 And

Isaac spoke unto Abraham his father, and said: 'My father.'

And he said: 'Here am I, my son.' And he said: 'Behold the

fire and the wood; but where is the lamb for a burnt-

offering?' 8 And Abraham said: 'God will provide Himself the

lamb for a burnt-offering, my son.' So they went both of

them together. 9 And they came to the place which God had

told him of; and Abraham built the altar there, and laid the

wood in order, and bound Isaac his son, and laid him on the

altar, upon the wood. 10 And Abraham stretched forth his

hand, and took the knife to slay his son. 11 And the angel of

the LORD called unto him out of heaven, and said:

'Abraham, Abraham.' And he said: 'Here am I.' 12 And he

said: 'Lay not thy hand upon the lad, neither do thou any

thing unto him; for now I know that thou art a God-fearing

man, seeing thou hast not withheld thy son, thine only son,

from Me.'

יצחק בנו, ויקח בידו, -עצי העלה, וישם על-ויקח אברהם את ו,כב

ויאמר יצחק ז,כב .יחדו; וילכו שניהם, המאכלת-האש ואת-את

אברהם אביו, ויאמר אבי, ויאמר, הנני בני; ויאמר, הנה האש -אל

לו -ויאמר, אברהם, אלהים יראה ח,כב והעצים, ואיה השה, לעלה.

המקום -ויבאו, אל ט,כב .יחדוהם, השה לעלה, בני; וילכו שני

-המזבח, ויערך את-לו האלהים, ויבן שם אברהם את-אשר אמר

המזבח, ממעל -יצחק בנו, וישם אתו על-העצים; ויעקד, את

, לשחט, המאכלת-ידו, ויקח את-וישלח אברהם את י,כב לעצים.

השמים, ויאמר, -ויקרא אליו מלאך יהוה, מן יא,כב בנו.-את

לח-אל, ויאמר יבויאמר, הנני. ;אברהם אברהם ש ך ת , המער-אל יד

אומה, לו תעש-ואל י עתה כי :מ ת ים ירא-כי, ידע ולא, אתה אלה

נך-את חשכת ך-את ב יד םמי, יח .מ

And those are “TUMIM” and “HaMeARRIM”.

Page 12: Hebrew Magic

“TUMIM” first appears in relation to Rivka, who was caring

twins, but have other meaning – as in “URIM” and “TUMIM”

- the oracle used in first the Temple. “HaMeARRIM” -

bringing curse – describes the “bitter water” given in the

Temple to the adulterous wife.

Though different, both words have common meaning of a

just judgment - a curse to the guilty and the blessing to the

just. Both devices were attributes of Cohen and used in the

first Temple. So, the similarity can hardly be random.

Twins, tricking, adultery. Rivka and Tamar.

25,21 And Isaac entreated the LORD for his wife, because

she was barren; and the LORD let Himself be entreated of

him, and Rebekah his wife conceived. 25,22 And the

children struggled together within her; and she said: 'If it be

so, wherefore do I live?' And she went to inquire of the

LORD. 10

25,23 And the LORD said unto her: Two nations are in thy

womb, and two peoples shall be separated from thy bowels;

and the one people shall be stronger than the other people;

and the elder shall serve the younger.25,24 And when her

days to be delivered were fulfilled, behold, there were twins

in her womb.

" בבטנה תומים והנה ללדת ימיה וימלאו " (Genesis).

10 The expression means usually asking God through “Urim and

Tumim”

Page 13: Hebrew Magic

Here “twins” is written in deficient form, so that its

gematria is equal to 496, the word itself being the same as

in “Urim and Tumim”.

Perhaps the word “תמים” (with aleph and vav omitted)

alludes also to Jacob, who is called TaMIM – either perfect

or timid.

Rashi following Midrash says that Rivka went to the Beit-

Midrash (house of study) of Shem to ask. Possibly in

Midrash Tumim number 496 is regarded not as perfect, but

as kind of curse, that the gematria of 496 (of “TUMIM” as of

“HaMeARRIM”-bitter OR cursed) is alluding to the curse, as

a curse after the transgression of Eva (and curse of Adam as

a result, too) in the sixth (and perfect) day of creation.

There indeed was a sort of curse in twins of Rivka – it is why

she went to house of study of Shem, which helps us seek

explanation in ancient tradition coming from

Shem=Malkizedek, the king of “Salem”, and he *is] Priest to

the God Most High.

Midrash seeks similar points in Rivka and Tamar, which can

explain why both gave birth to twins. So it says, the scarf -

“ZʼIF” - of Rivka and Tamar signifies their double- faced

behavior – tricking. The (possibly unconscious) line of

thought, which links TUMIM with HaMeARRIM (both 496),

continues to ask – how come Torah uses the cursed number

with relation to her? Of course she was adulteress – she

uses the scarf!

Let’s examine the Torah passage in the book of Numbers (5)

about a sota, a pervert woman, to whom the whole tractate

is dedicated.

Page 14: Hebrew Magic

Sota – adulterous woman, the water and the Cohen11

ואמרת, ישראל בני-אל דבר יב,ה .לאמור משה-אל, יהוה וידבר יא,ה

איש ושכב יג,ה .מעל בו ומעלה, אשתו תשטה-כי איש איש :אליהם

אין ועד; נטמאה והיא ונסתרה, אישה מעיני ונעלם, זרע-שכבת, אותה

והיא, אשתו-את וקינא קנאה-רוח עליו ועבר יד,ה .נתפשה לא והיא, בה

טו,ה .נטמאה לא והיא, אשתו-את וקינא קנאה-רוח עליו ברע-או; נטמאה

עשירית, עליה קרבנה-את והביא, הכוהן-אל, אשתו-את האיש והביא

מנחת-כי--לבונה עליו ייתן-ולא, שמן עליו ייצוק-לא; שעורים קמח האיפה

; הכוהן, אותה והקריב טז,ה .עוון מזכרת זיכרון מנחת, הוא קנאות

; חרש-בכלי, קדושים מים הכוהן ולקח יז,ה .יהוה לפני, והעמידה

-אל ונתן, הכוהן ייקח, המשכן בקרקע יהיה אשר, העפר-ומן

-את ופרע, יהוה לפני, האישה-את הכוהן והעמיד יח,ה .המים

; היא קנאות מנחת הזיכרון מנחת את כפיה-על ונתן, האישה ראש

אותה והשביע יט,ה .המאררים המרים מי, יהיו הכוהן וביד

שטית לא-ואם, אותך איש שכב לא-אם האישה-אל ואמר, הכוהן

כ,ה .האלה המאררים המרים ממי, הינקי--אישך תחת, טומאה

, שכובתו-את בך איש וייתן; נטמאת וכי--אישך תחת שטית כי, ואת

, האלה בשבועת, האישה-את הכוהן והשביע כא,ה .אישך מבלעדי

--עמך בתוך ולשבועה לאלה אותך יהוה ייתן, לאישה הכוהן ואמר

11 Oil painting reproduction “Sephardi woman” by

O.Youssin

Page 15: Hebrew Magic

המים ובאו כב,ה .צבה בטנך-ואת, נופלת ירכך-את יהוה בתת

ואמרה; ירך ולנפיל, בטן לצבות, במעייך, האלה המאררים

; בספר--הכוהן, האלה האלות-את וכתב כג,ה .אמן אמן, האישה

, המרים מי-את, האישה-את, והשקה כד,ה .המרים מי-אל, ומחה

הכוהן ולקח כה,ה .למרים, המאררים המים בה ובאו; המאררים

, יהוה לפני המנחה-את והניף; הקנאות מנחת את, האישה מיד

-את המנחה-מן הכוהן וקמץ כו,ה .המזבח-אל אותה והקריב

-את, האישה-את ישקה ואחר; המזבחה והקטיר, אזכרתה

מעל ותמעול נטמאה-אם והייתה, המים-את והשקה כז,ה .המים

ונפלה בטנה וצבתה, למרים המאררים המים בה ובאו--באישה

נטמאה לא-ואם כח,ה .עמה בקרב, לאלה האישה והייתה; ירכה

, תורת זאת כט,ה .זרע ונזרעה, וניקתה--היא וטהורה, האישה

, איש או ל,ה .ונטמאה, אישה תחת אישה תשטה אשר, הקנאות

-את והעמיד; אשתו-את וקינא--קנאה רוח עליו תעבור אשר

לא,ה .הזאת התורה-כל את, הכוהן לה ועשה, יהוה לפני, האישה

}פ{ .עוונה-את תישא, ההיא והאישה; מעוון, האיש וניקה

5,17 And the priest shall take holy water in an earthen

vessel; and of the dust that is on the floor of the tabernacle

the priest shall take, and put it into the water. 5,18 And the

priest shall set the woman before the LORD, and let the hair

of the woman's head go loose, and put the meal-offering of

memorial in her hands, which is the meal-offering of

jealousy; and the priest shall have in his hand the *1 water

of bitterness that causeth the curse. 5,19 And the priest

shall cause her to swear, and shall say unto the woman: 'If

no man have lain with thee, and if thou hast not gone aside

to uncleanness, being under thy husband, be thou free from

this *2 water of bitterness that causeth the curse; 5,20 but

if thou hast gone aside, being under thy husband, and if

thou be defiled, and some man have lain with thee besides

thy husband-- 5,21 then the priest shall cause the woman to

swear with the oath of cursing, and the priest shall say unto

Page 16: Hebrew Magic

the woman--the LORD make thee a curse and an oath

among thy people, when the LORD doth make thy thigh to

fall away, and thy belly to swell; 5,22 and this *3 water that

causeth the curse shall go into thy bowels, and make thy

belly to swell, and thy thigh to fall away'; and the woman

shall say: 'Amen, Amen.' 5,23 And the priest shall write

these curses in a scroll, and he shall blot them out into the

5,24 And he shall make the woman drink the *4 water of

bitterness that causeth the curse; and the *5water that

causeth the curse shall enter into her and become bitter.

5,25 And the priest shall take the meal-offering of jealousy

out of the woman's hand, and shall wave the meal-offering

before the LORD, and bring it unto the altar. 5,26 And the

priest shall take a handful of the meal-offering, as the

memorial-part thereof, and make it smoke upon the altar,

and afterward shall make the woman drink the water. 5,27

And when he hath made her drink the water, then it shall

come to pass, if she be defiled, and have acted unfaithfully

against her husband, that the *6water that causeth the

curse shall enter into her and become bitter, and her belly

shall swell, and her thigh shall fall away; and the woman

shall be a curse among her people. 5,28 And if the woman

be not defiled, but be clean; then she shall be cleared, and

shall conceive seed. 5,29 This is the law of jealousy, when a

wife, being under her husband, goeth aside, and is defiled;

5,30 or when the spirit of jealousy cometh upon a man, and

he be jealous over his wife; then shall he set the woman

before the LORD, and the priest shall execute upon her all

this law. 5,31 And the man shall be clear from iniquity, and

that woman shall bear her iniquity. {P}

The water is called ‘sacred ‘first time, then 6 more times

(perfect number) it is called HaMeAReRIM, which is 496 in

Page 17: Hebrew Magic

gematria. At first glance, it can be hardly an accident. But

according to some linguistic researches (though mostly of

English language) there is a certain predictability of word

forms.12 However, that predictability, is in our opinion de

facto, which is to say that without further research, we can

postulate, that occurrence of certain words with gematria

496 will be 6 exactly in different Hebrew Bible books.

12 See for example.

“Using probability distributions to account for recognition of cano

nical and reduced word forms”

Meghan Clayards, Centre for Research on Language Mind and Brai

n, McGill University, Montreal, Quebec

Canada,

“Speech production and the predictability of words in

context “,Frieda Goldman-eisler, The Quarterly Journal of

Experimental Psychology, Volume 10, Issue 2 May 1958 , pages 96

– 106

Page 18: Hebrew Magic

Sarah . Sarah’s age at death, which is 127=27 -1 is basis of perfect number

(because 27 -1 =127 is prime), which is

Rashi following Midrash says that Sarah was as beautiful as a seven year old.

Which always presented some problem, and we left that as it was. But if

beautiful as seven years old means just the same as 497 years old, at least

we do not have difficulty in suspecting Rashi in nymphomania. Gematria of

“XaIeI” (life of somebody) חיי is 28, which is perfect, moreover, this word

we met exactly 6 times in the Genesis -2 times in relation to death of Sarah

(23:1), once in relation to death of Abraham(25:7) and Ishmael (25:17) and

twice in relation to death of Jacob in Egypt (47:9). 13

13 In Exodus – three times in relation to death of Levi (6:16),

Kehat (6:18), Amram (6:20):

(27 -1) *26=8128

Page 19: Hebrew Magic

כג,א ויהיו חיי שרה, מאה שנה ועשרים שנה ושבע שנים—שני .

חיי שרה

רהם—אשר-חי ני-חיי אב כה,ז ואלה, ימי ש

ים שנה, ושבע לש את שנה וש מעאל--מ ני חיי יש כה,יז ואלה, ש

יועם -אל ויאסף, וימת ויגוע; שנים .

עה-אל, יעקב ויאמר ט,מז ני ימי, פר גורי ש ים, מ לש את ש ומ

ני חיי יגו את-ימי ש ש ני חיי, ולא ה ים, היו ימי ש עט ורע שנה: מ

ימי, אבתי גוריהם ב מ .

If we take into account complex relations of our forefathers

with Egypt – Abraham and Sara's stay in Egypt in times of

the famine, Sara' staying at Pharaoh, birth of Ishmael from

Hagar- the Egyptian slave, Joseph's selling to Egypt and

Jacob's ascending there, we can probably suggest that those

occurrences are in fact Egyptian-isms. Isaac went never to

Egypt.

According to Jewish tradition, the Hebrew alphabet was

given at revelation and Torah. How they were writing

numbers prior to Sinai?

נ י י; וש רר הת ומ שון, וק דתם--גר תל ני-לוי, ל מות ב ו,טז ואלה ש

את שנה ים ומ לש .חיי לוי, שבע וש

הת, ני חיי ק רון ועזיאל; וש רם ויצהר, וחב הת--עמ ני ק ו,יח וב

ים שלש לש את וש שנה ומ .

רם חויק כ,ו שה לו, דדתו יוכבד-את עמ א אהרן-את, לו ותלד, ל

את שנה ים ומ לש רם, שבע וש ני חיי עמ .ואת-משה; וש

It does not appear in other Torah books.

Page 20: Hebrew Magic

The fourth perfect number 8128. Kingdom

Though this research is focused mainly on 5 Torah scrolls, as

we need to check whether the use of perfect numbers was

kind of Egyptian-isms, we decided to see in the whole of

Hebrew Bible for bigger perfect numbers.

The gematria of Kingdom (מלכות) is 496 – important, but

does not appear in this form in 5 books of Moshe.14

For searching occurrences of the perfect number 8128 we

used the Bar-Ilan computer program15, to find a sentence or

part of it with sum of gematria of consecutive words 8128.

(The next perfect number after 8128 is too big to be part of

a sentence.)

There were two occurrences in the Bible, both – in relative

proximity, we read also what is between - in the book of

Kings:

ד פסוק יח פרק ב מלכים. 1

עשה אשר המחשת נחש וכתת האשרה את וכרת הםצבת את

ים עד כי משה ני היו ההםה הימ ראל ב ים יש ר קט רא לו מ לו ויק

תן נחש

Kings 2: 18:4

udah) removed the He (Hezekiah the son of Ahaz king of J

high places, and broke the pillars, and cut down the

Asherah; and he broke in pieces the brazen serpent that

Moses had made ;

14 in this form appears, for example 6 times in the "מלכות"

Chronicles.

15 Bar-Ilan University SHUTIM project, version 14

Page 21: Hebrew Magic

and ;for unto those days the children of Israel did offer to it

it was called Nehushtan.

The verse is about how the righteous King Hezekiah – who

could be a Messiah, - deals with the magic brazen serpent

which remained from the times of Moshe. (See Numbers

2116) So our modern concept of Messiah – the revolutionary,

as in the poem “12” by Russian poet from the time of

communist revolution Alexander Block, is right: the

Messiah-the revolutionary destroys the idols of predecessor

(though sometimes also the art and the culture)

This verse brings to a definite end theory of the primordial

sin of Eva as a cause for all human suffering as it no longer

imply woman but the Serpent as a source of sin and evil.

It is also clear, as a parable of God’s creation of serpent, evil,

“big Leviathan”, Crocodile, Dragon etc., that an evil was

16 4.”And they journeyed from mount Hor by the way to the Red

Sea, to compass the land of Edom; and the soul of the people became

impatient because of the way. 5 And the people spoke against God, and

against Moses: 'Wherefore have ye brought us up out of Egypt to die in

the wilderness? for there is no bread, and there is no water; and our soul

loatheth this light bread.' 6 And the LORD sent fiery serpents among the

people, and they bit the people; and much people of Israel died. 7 And

the people came to Moses, and said: 'We have sinned, because we have

spoken against the LORD, and against thee; pray unto the LORD, that He

take away the serpents from us.' And Moses prayed for the people. 8 And

the LORD said unto Moses: 'Make thee a fiery serpent, and set it upon a

pole; and it shall come to pass, that every one that is bitten, when he

seeth it, shall live.' 9 And Moses made a serpent of brass, and set it upon

the pole; and it came to pass, that if a serpent had bitten any man, when

he looked unto the serpent of brass, he lived”

Page 22: Hebrew Magic

made or created– and not co-existent with God from

primordial times – for some good purposes, but can be

controlled. Notice, that in Sukkot prayer we ask to sit in the

future in Jerusalem in Sukkah made from the leather of

Leviathan. ( = 496לויתן)

ג פסוק כג פרק ב מלכים. 2

ית ר ני הב פ מר יקוק אחר ללכת קוקי ל ש ותיו ול צ ותיו ואת מ ואת עד

כל חקתיו כל לב ב ים נפש וב הק רי את ל ב ית ד ר ים הזאת הב הכתב

העם כל ויעמד הזה הןפר על

Kings 2: 23:3

And the king (in the eighteenth year of King Josiah) stood on

the platform, and made a covenant before the LORD, to

walk after the LORD, and to keep

His commandments, and His testimonies, and His statutes,

with all his heart, and all his soul, to confirm the words of

this covenant that were written in this book; and all the

people stood to the covenant.

---------------------------------------

This second verse is about sort of a covenant made by the

King Josiah, after discovering the book of Torah in the

Temple by High Priest at the time of repairing-maintenance

of the Temple. (Apparently it was lost or destroyed by

previous idolatrous king – see Kings 2 chapters 18-23).

By the way, the scribe and the High Priest, the most

important heroes in the current paper, make the discovery.

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It was impossible to find those verses without software, but

possible to encode, whoever did it – the prophet Jeremy

wrote the book. In fact, why should those verses be

important – possibly because the Torah was once lost and

could be lost again.

The names of small animals of three of main personages are

a little puzzling – we have the rabbit the scribe, the rat the

prophetess and the mouse the secretary, as if their names

taking all of importance of their position, the council of the

mice.

So research about the chain of perfect numbers, proving in a

way authenticity of the Hebrew Bible, comes to end, the full

an analysis of the story of how the High Pries Hilkiah and the

scribe Shaphan have found or rewritten the book is beyond

the scope of this paper.

Conclusions

496= testing by perfectness

Philo was obviously a Hellenist. The sixth day would be

perfect – but ...The sixth day in Jewish tradition is associated

also with Adam and Eva, Eva's speaking to the snake and

eating from the forbidden fruit, expulsion from the Eden,

Curse of Eva in childbirth and being ruled over by the man,

and curse of man in his labor of the Earth. The mentioned

perfect numbers were associated with the curse of Eva in

early traditions...

Here are a few hypotheses.

- The problem : according to Liberman, Gematria was a

Hellenistic innovation (Liberman. Hellenism) ~323 BC, but

Page 24: Hebrew Magic

as, according to oral tradition, the alphabet in its order was

already known or given at the Sinai with Torah,17 the Scribesi

could use the gematria long before that. If so, the linguists,

working on proving that the possible proto-language is some

ancient form of Hebrew18, which has a divine origin, would

gain the numbers, arithmetic or even some kind of number

theory, which the people of Israel received in the same

package.

- Or is it possible that some of early traditions from the

Flood time, where Shem and Japheth had the same

alphabet, were included in Torah (“Torah was given scroll

after scroll”).with gematria, forgotten but reintroduced in

times of Hellenism? Not according to Wikipedia.

- The other possibility is, it could be that any meaning which

appears here was really not there. Information theory does

not prohibit "noise" from appearing to be sometimes

meaningful. Some unusual patterns can randomly appear.

We needed to define statistical test in advance in order to

determine if those results exhibit patterns that overcome

the level of noise .

17 Changes in Torah made by scribes, who copied the Torah

scrolls. According to Liberman in “Hellenism”, following early

sources, there are two different opinions regarding the “Tikkun

sofrim” – corrections of scribes. One is that the scribes corrected a

few specific places in Torah so as to eliminate „dirty‟ language in

relation to the high. The other – that the scribes wrote the Torah in

this way originally (corrected in place).

18 References to origin of language

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- Other attempt to explain it is, that those “Hellenisms”

were introduced as a reminder of the beauty of the Jewish

woman and danger in such beauty, instead of Goddess

Aphrodite (statues of Aphrodite were present in ancient

Israel – and mentioned in Mishnah), and later the same

instrument of gematria by factorization of a word and

combining from dividers other words as “signs”, was used

in creation of Jewish halacha as well.

In traditional Judaism the myth of Eva's transgression as a

source of evil is replaced with more philosophical and non-

magic view. The “feminine” is demystified and becomes

more of a companion. The serpent is demystified and evil

becomes small and easy to overrule.

TUMIM and bitter water will not be in the Second Temple.

The gematria and factorization of words as method for

remembering things and deriving additional clues where

there were none and where it does not matter (it does not

matter, for example strictly speaking how many forbidden

works in Sabbath there were, as long as there is some sort

of system and limits)

In the piutim for Shabbat, Israel is called “the nation which

sanctifies the seventh”, which could mean not only seventh

day – Shabbat, but any seventh. The seventh year –

“SMIiTa”, when the fruits have a “kdushat shviit| - “seventh

sanctity”, numerous examples of sanctifying or purifying

from various impurities, involving Cohen, frequents in

Leviticus and Numbers.

Page 26: Hebrew Magic

So, there probably are some more-than-perfect numbers,

too.

We lack the 496+1. Let's seek it.

Sabbath and Melacha – some calculations of words/laws

using gematria.

In Tractate "Shabbat" we learn that there are 39

"mel'achot" - kinds of work, which is forbidden to perform

on Shabbat, for example building, coloring etc. Why this

number - because there are 40 occurrences of the world

"Mel'acha" - work, in the Torah (in some specific

wordforms), or maybe 41 according to other saying.19

19

תלמוד בבלי מסכת שבת דף מט עמוד ב

ארבעים מלאכות אבות דתנן הא: להו וקמיבעיא יתבי הדור

. המשכן עבודות כנגד: חמא בר חנינא רבי להו אמר? מי כנגד אחת חסר

: לקוניא בן יוסי ברבי שמעון רבי אמר כך אלעזר ברבי יונתן רבי להו אמר

רב בעי. אחת חסר ארבעים - שבתורה ומלאכת מלאכתו מלאכה כנגד

? לא או, הוא ממנינא מלאכתו לעשות הביתה ויבא +לט בראשית+: יוסף

חנה בר בר רבה אמר לא מי! ולימני תורה ספר וליתי: אביי ליה אמר -

: ליה אמר. נאוםומ תורה ספר שהביאו עד, משם זזו לא: יוחנן רבי אמר

דים היתה והמלאכה +לו שמות+ דכתיב משום - לי מספקא קא כי

ויבא: דילמא או, נכנס צרכיו לעשות דאמר כמאן - והא, הוא ממנינא

הכי - דים היתה והמלאכה והאי, הוא ממנינא מלאכתו לעשות הביתה

עבודות כנגד דאמר כמאן תניא. תיקו? עבידתא ליה דשלים: קאמר

הם, במשכן היתה בה שכיוצא מלאכה על אלא חייבין אין: ניאדת, המשכן

את העלו הם, תקצרו לא ואתם - קצרו הם, תזרעו לא ואתם - זרעו

לרשות הרבים מרשות תכניסו לא ואתם - לעגלה מקרקע הקרשים

תוציאו לא ואתם - לקרקע מעגלה הקרשים את הורידו הם. היחיד

לא ואתם - לעגלה מעגלה הוציאו הם, הרבים לרשות היחיד מרשות

מאי, היחיד לרשות היחיד מרשות. היחיד לרשות היחיד מרשות תוציאו

: אהבה בר אדא רב ואיתימא, תרוויהו דאמרי ורבא אביי -? עביד קא

הרבים רשות דרך היחיד לרשות היחיד מרשות .

Page 27: Hebrew Magic

The passage decides, that phrase about the God, who rests

from his work ("Mel'achto") on the 7-th day, and the phrase

about Joseph, who, after "sexual harassment" of the wife of

Potiphar, returned to do his work ("Mel'achto") do not

count because those occurrences have other meanings. In

continuation of discussion the sages abundantly use

gematria. (Perhaps, the number of works-mel’acha – was

already predefined)20

20gematria of Shabbat is 702=18*39

300+2+400 = שבת

חי (alive, living being in Hebrew – important thing in Judaism,

gematria of the word is 18)

sin, transgression; the word “hataat” – sacrificial) חטא

offering in case of unintentional transgression – has the

same root) has gematria of 18 too.

Is 300+2+400=702=18*39, where 18 is gematria of HI,

‘live’ in Hebrew; and one of most important principles of

observing Shabbat is to violate its laws in order to save life, as it is

written “and you should live in them” (the commandments).

Additionally, 18 is the gematria of “Het” – transgression, and from

here we can deduce also the rule that the number of forbidden

works (just for classification, many other prohibitions considered

to derive from those main 39 root laws) was fixed to be 39

because gematria of Shabbat is 702=18*39. We find theproof of

our argument in the following sentenceses:

Anyone, who knows about Shabbat, its interdictions and

performing many transgressions, is guilty of every one of them –

must bring sacrificial offering in times of Temple (for each one ).

(Mishnah Shabbat)

But usually gematria in modern days is regarded as joke, like the

one I heard from rabbi Haiim Meir Kahane, a Viznitz Hassid, a

Cohen, who was imprisoned in Siberian Soviet camps for years.

Page 28: Hebrew Magic

The whole passage seems to put some additional and

mutual meaning in "Mel'achto" of God and of Joseph. In

both cases the word does not mean real human work. In

case of Joseph it is just a reference to his affair with the wife

of Potiphar, meaning his – spared at the end - sexual act

with her. The sexual act is one way of sanctifying a woman.

In case of God it is obviously not human work, but perhaps,

in light of a cabbala, or “breaking of the vessels” conception,

is also some kind of divine sacred act, sanctifying of the

reality by performing kind of intercourse with it. The

gematria of “Mel’achto” is 497=496+1. The next after the

perfect number. The God sanctified Shabbat after

performing his "Mel'achto".

The Scribes. Letter –arithmetics.

Edward Belaga and (independently) some people in Bar –

Ilan University (see for example “ פאי ערכים מדוייקים של

21wrote articles about a π number ”( במקורות היהדות

encoded in the book of Kings, when the ration of “Kri” to

“Ktiv” gives a most outstanding approximation for the

Rabbi Kahane treated me as Shabbat guest to kugel: “you

know why you should eat kugel? Because it equals Shabbat in

gematria.”

“Not at all! Its gematria is much less than Shabbat!”

“Then take some more kugel”

Though not gematria, but the perimeter or the surface

area or the volume of kugel (which is a round cake ) is a

transcendent number, perhaps as transcendent as a Shabbat.

21 http://u.cs.biu.ac.il/~tsaban/Pdf/exactpi.pdf

Page 29: Hebrew Magic

irrational (and transcendent22 ) number π– the perimeter of

a circle with radius 1. Again this “Kri” and “Ktiv” – the read

(written as a comment) and “Ktiv” – the written words are

found in the verses related to the building of the Temple.

This fact brings us to the suggestion, that those fully and not

fully vocalized words were encoded for some purpose

perhaps by scribes. (Tikkun Sofrim23?) The play with full or

omitted vowels permits a multi-dimensional meaning when

using gematria. It is not to say that scribes introduced some

mathematical calculation while changing Torah text, but just

that many Jewish religious laws and thoughts are

incorporated in those plain-missing vocalization,

transliteration, and gematria. That however, was not

explicitly written elsewhere, specifically not - complex,

perhaps factorizations of significant numbers.24 But this

analysis proves that such a work was going on.

If perfect numbers were known, than in addition to

“addition” method, used in cabala, which combines

gematria of few words so that the sum will be equivalent to

22

Irrational number is a number which cannot be presented

as a fraction, as for example √2, while transcendent is a number,

which is not algebraic – is not root of any algebraic equation, as is

number π

23 Liberman

See 4

24 There is no use for “gematria” of words as factorization

(for example. SBT(702)=TL(39)*HI(18)) in late Jewish sources, only

use of gematria for purposes of decomposition word as sum of

other words, with exception of passage in Sefer Yezira, where it is

mentioned that some word “beats” the other, in sense, its

gematria is divisible by gematria of the other word.

Page 30: Hebrew Magic

the gematria of some other word, as means of commentary,

we have a multiplicative letter arithmetic. It is quite possible

that some known laws and ideas were incorporated by that

way in Mishnah, if we had such oral tradition – and some of

Jews perhaps have it, we could try to unveil the whole

Mishnah or Midrash with use of this instrument.

Let’s demonstrate how a gematria conveys an additional or

even opposite meaning.

The mercy of God, though we“ (Psalms) ”חסדי ה' כי לא תמנו“

did not were perfect “. After calculating TaMNU=496 which

is perfect number we see that perhaps we were perfect, at

least in God’ eyes.

TMIMA=495=496-1. Gematria conveys us a contrary

meaning that Torah misses one to be perfect, or that Torah

is perfect while missing one, which is a meaning of Midrash

“Better that Torah will lose one letter, than the name of God

be desecrated publicly”, which in turn means that in the

danger of desecration of God’s name it may be sometimes

permitted to cancel one of the laws. (Libermann)

Conclusion: Canonization of Hebrew Scriptures

So, either way it seems, that there was a”numeric magic” in

Torah of Moshe (perhaps – against numeric magic of Egypt),

which was abolished and maybe called “Hellenism” by

modern scholars. Otherwise we have to decide that (final?)

canonization of Hebrew Scriptures took place somewhere

in time of Hellenism; and perfect numbers (among other,

possible complex Masoretic traditions ) were points of

“signing” of the Bible, so that there would be some easy

checks of the authenticity of the final version. ii

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Appendix: table of numerical values of letters in gematria

א1

2 ב

3 ג

4 ד

5 ה

6 ו

7 ז

8 ח

9 ט

10 י

20 כ

30 ל

40 מ

50 נ

60 ס

70 ע

80 פ

90 צ

Page 33: Hebrew Magic

Appendix 1.

The numeric puzzle

The most famous song for woman (long accepted here as an

allegory to Wisdom, Shechina, Torah) which is recited on

Sabbath eve is “Eshet Hail” (“The woman of glory”, end of

“Parables” of King Solomon).

The Hebrew Alpabet does not appear anywhere in Bible

before Psalms25, some of which are structured in form of

Alphabetical verses.26 Let’s assume that we do not have a

25 The 176 verses of Psalm 119 are in Alphabethical order, while

each letter is repeated 8 times. The verses of Psalm 145 – just one

time.

26 and it is the reason why the piut „Akdamot“, which has all its

verses in alphabethical order, is recited in Synagogues on Shavuot

- the festival of Torah revelation,

“ after Kohen has been called to the Torah, but before he recites

his blessing...Composed by rabbi Meir ben Itzhak (11 century,

Worms, Germany) ...written in a difficult Arameic ... its first 44

verses form a double acrostic of the Aleph-Bet...Each verse is

concluded with suffix תא, the last and first letters of Hebrew

Aleph-Beth.“ (The complete Artscroll Siddur).

Here we have perhaps another mathematical idea, appropriate

for the time. If we arrange letters around the circle,

a. the letters can be regarded as vectors

b. the letters can be regarded as complex numbers

c. the sum of all letters is equial to 0

800 ת"ת

900 תת"ק

1000 תת"ר

Page 34: Hebrew Magic

specific Alphabet order, neither gematria yet. We want to

create a “magic” effect, where some important objects have

a “perfect number” value. The Hebrew Oral Tradition,

though, asserts, it came at times of Moisey revelation on

mount Sinai.

*see about hebrew Aleph-Beth in Jewish sources and in

Wikipedia

If the order of hebrew 22 letters was fixed at some time, the

gematria could be also easily fixed, by assigning to first 9

letters numbers 1-9, than 10-90, and finally 100-400 to the

rest. Whoever did it, some sage or priest, if it was not fixed

at the time of receiving Torah, could have either special

guidance or some possibly secret intentions, why assign 1 to

Aleph and 2 to Beth.

( while it does not matter which letter is first or second..).

If we take into account that important philosophic idea of a time,

that the world was created „ex-nihilo“, and another cabbalistic

idea about creation with letters, and combine those ideas, we can

almost visualize that creation of things arranged in some order,

like some mathematical unknots – trivial knots, f.e famous „ סולם

a tricky knot, which becomes just circle, when dragged ,“יעקב

someplace.

Page 35: Hebrew Magic

Gematria is used to say something like „word A is the same

as word B in gematria“, employing these words are related

and are various presentation of the same number.

While researching perfect gematria in Torah, and have

found that gematria of some important words (cleary visible

or repeated, but rare) was 496. Assuming, that somebody,

who assigned the order of letters and defined gematria, had

in mind to show or encrypt some special words, -and some

other words could have the same values by accident, we

find that

694המאררים=תומים=מלכות=

The first two are attributes of Kohen (High priest) in two and

only almost magical rituals27, which involve priests, the

third – the king.

The mathematical rebus, which perhaps Somebody thus

cleverly resolved, is a simple ancient linguistic puzzle, but as

the resulting value is a perfect number, and perfect number

6 and probably 28 play some significant role in priestly

rituals.

The Torah, however, in this Alpabethical order begins with

the second letter, the fact to which numerous Midrashim

had to seek an explanation.

The word „my life“ appears six times in Genesis, so perhaps

its value was 28

82חיי=

Page 36: Hebrew Magic
Page 37: Hebrew Magic

Appendix 2

Urim and Tumim – multiple choice statistical game?

God maybe does not play dice28 (as Einstein put it), but Jews

do!

Prof.Eli Merzbach (probabilities& statistics) had answered

question about it in newspaper. He basically said that from

statistics point of view it is highly improbable to receive a

"TRUE" answer by it (he actually had calculated that

probability, which was like probability to win a lottery).

Perhaps, he thought, that by that he was affirming that it

was a miracle. So he brought us to think about Urim and

Tumim as a divine instrument, which miraculously

prescribed the right course of action.

And, if so, perhaps the precious stones, from which if was

made, were doing the task, as the alchemists would think.

But there is another look at it as a probabilistic game, when

the player receives a blessing to go in the particular way

that he got in a game.

Perhaps, it is a many centuries dispute.

According to the Babylonian Talmud 29 , Urim and Tumim

where used just to make a decision very much like court

decision whether to act in some way or the other, the

results of the action were not automatically guaranteed, so

28 Einstein did not accept probabilistic or non-deterministic

description of God governing the Universe. See, for example

correspondence between Einstein-Bohr.

29 See, for example Babylonian Talmud, Adin Steinsaltz’s

commentary for Ioma

Page 38: Hebrew Magic

the Cohen used his Holy spirit to interpret the reading. So, in

fact, it could be that the Urim and Tumim was a machine for

making a choice in multiple choice game, where different

options could have different weights. The king through

Cohen was playing a fortune game, while assigning various

probabilities to different outcomes - reasonable

probabilities to win while choosing various ways of action,

and it was probably a Cohen who was manipulating the Holy

instrument and assigning realistic probabilities.30

תלמוד בבלי מסכת יומא דף עג עמוד ב 30

שלא ששאל שידע וכיון. כסדר לו והחזירו, כסדר שלא

בעלי היסגרו+ כג' א שמואל+ שנאמר, כסדר ושאל חזר - כסדר

צרךהו ואם. יסגירו' ה ויאמר שאול ביד אנשי ואת אתי קעילה

וישאל+ ל' א שמואל+ שנאמר, שנים לו מחזירין - לשנים הדבר

לו'( ה) ויאמר האשיגנו הזה הגדוד אחרי ארדף לאמר' בה דוד

, חוזרת נביא שגזירת פי על ואף, תציל והצל תשיג השג כי רדף

במשפט+ כז במדבר+ שנאמר, חוזרת אינה - ותומים אורים גזירת

את שמאירין - אורים? מיםותו אורים שמן נקרא למה. האורים

בגבעת: תאמר ואם. דבריהן את שמשלימין - תומים, דבריהן

אם לנצח אם ביחנו שלא הם -? השלימו לא מה מפני בנימין

ופינחס+ כ שופטים+ שנאמר, הסכימו - שביחנו ובאחרונה להנצח

לצאת עוד האוסף לאמר ההם בימים לפניו עמד אהרן בן אלעזר בן

אתננו מחר כי עלו' ה ויאמר אחדל אם אחי נימןב בני עם למלחמה

: אומר לקיש ריש, בולטות: אומר יוחנן רבי? נעשית כיצד. בידך

: יצחק בר שמואל רב אמר -! י"צד בהו כתיב לא והא -. מצטרפות

רב אמר -! ת"טי כתיב לא והא -. שם כתיב ויעקב יצחק אברהם

שאינו כהן כל: מיתיבי. שם כתיב ישורון שבטי: יעקב בר אחא

שאל שהרי, בו שואלין אין - עליו שורה ושכינה הקודש ברוח מדבר

+ טו' ב שמואל+ שנאמר, לו עלתה ולא אביתר, לו ועלתה צדוק

ואין. בהדייהו מסייע הוה סיועי -'. וגו העם כל תם עד אביתר ויעל

קרא דאמר: אבהו רבי אמר? מילי הני מנא. למלך אלא שואלין

האורים במשפט לו ושאל יעמד הכהן אלעזר ולפני+ כז במדבר+

וכל, מלחמה משוח זה - אתו ישראל[ בני] וכל, מלך זה - הוא' וגו

. גדול כהן לו בא עלך הדרן. סנהדרין זו - העדה

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i See http://en.wikipedia.org/wiki/Masoretic_Text

ii See http://en.wikipedia.org/wiki/Development_of_the_Jewish_canon

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Appendix 3.

Can Elisha use the axiom of choice?31

31 The axiom of choice is the axiom in mathematical Set

theory, not accepted by all mathematicians, basically it assumes,

that if you have a multitude of non-empty sets, you can choose an

element from each one of them. The proof of Banach-Tarsky

theorem is based on the axiom of choice.

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Here is one of the most important miracles in Judaism at

Hellenistic period that can be of interest to mathematicians –

Hanukkah’s miracle of oil in the Temple.

Are all miracles mathematically justified?32

32 Mathematics being a priory, remains unchanged in any

possible world

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It seems, the Hanukkah’s miracle is. Indeed according to the

Banach-Tarsky paradoxical theorem, it is possible, believe it or

not, to cut an orange33 into finite number of pieces that can

be rearranged to produce two oranges, the same size and

volume as the first. One can easily obtain from here the other

miracles of a kind. (Seeing any quantity of oil as many

spherical drops). (The theorem uses “Axiom of choice”, not

universally accepted.)

It is different with two-dimensional surfaces: it is impossible

to cut a circle, for example, and 34combine two circles the

same size from its parts

It being the case, it is clear, why one cannot, even

theoretically, multiply paper money, 35except by coping it !

Apart from paper money we can imagine the textile roll

unrolling and cut to million pieces of material, for this we

certainly need another theorem, and the process seems

definitely Arab, perhaps they have some corresponding

mathematical proposition .

33 Actually, the theorem is about identical spheres.

34 This impossibility results from the fact, that you can always

define a measure on any two-dimensional set; and obviously the

area of a circle is less than the combined area of two such circles,

which is not the case with three dimension objects: there you can

cut (theoretically) an object in immeasurable parts

35 Our own intuitive reason for it being impossible is that by

multiplying money you actually do not create goods (possibly all

goods must be 3-dimensional in this world, which the money said to

represent, so it is not a miracle, it is a fraud!

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The first oil (or maybe second, if we count the similar food

miracle of the prophet Elijah in Kings 1, 17: 8-16 ) miracle in

the Bible occurs in Kings 2, 4:1-7. One important probably

point is that both miracles (Elisha' and Hanukkah’s) were

performed with oil – which usually serves for sacred

purposes, as for lighting Menorah in the Temple or lighting

Sabbath or Festival candles at home. The other important

point is – that the oil was multiplied (in case of Elisha) or

maybe made longer-lasting (in Hanukkah’s case) from an

existing amount of oil.

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Bibliography

[1]Saul Liberman “Greek and Hellenism in Jewish Palestine”

[2] Sid Shnayer Z. Leiman “The Canonization of Hebrew Scripture: The Talmudic and

Midrashic Evidence “

[3] Babylonian Talmud

[4] The Hebrew Bible

[5] Canon and Masorah of the Hebrew Bible, An Introductory Reader

[Library of Biblical Studies series

*6+ Lee Martin McDonald, James A.Sanders “The Canon Debate”

[7] Michael A. B. Deakin and Hans Lausch "The Bible and Pi" The

Mathematical Gazette

July 1998 Volume 82 Number 494

"מקור ראשון" [8]

*9+ Osnat Youssin “Morphi – the universal morphological analyzer, software”,

Blue&White, 1999, Jerusalem – Max Plank, Leipzig

*10+ Yael Shemesh “Elisha and The Miraculous Jug of Oil” The Journal of

Hebrew Scriptures,

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Appendix 4

Introduction

We have heard about TC (=Torah Codes) more than 20 years ago, while

participating in some Torah Seminar .

About 8 years ago we planned to write software dialing with TC, but soon

after that such a tool already appeared in the market, with a booklet, in which

it was promised prediction of future events with its aid.

This article analyzes the claims and explains results of research in TC on 3

levels:

Mathematical (probability, statistics)

Linguistic (meaning, mathematical methods in linguistics)

Jewish – Philosophic – Halacha

Basically, TC is reading Torah with some step, for example every 5-th letter

beginning from 123-th letter. (See for example Wikipedia article on Torah

Codes) The history of this idea is not completely known, but recently - in

previous century - some mathematicians took interest in this. Some wrote

scientific articles (for example Eliahu Rips). Few claims, based on experiments,

about such reading were made.

There appeared many related words and phrases in near proximity with

corresponding Torah passages (such as ‘ahava’ – love, in the story of Adam

and Eve)

One can find any important event, people, and so on, while reading with

an appropriate step.

It is possible to predict a future by such means (this claim does not

however appear in writings and is completely rejected by founders of TC and

is only supported and propagated by the software vendors)

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The question is: how to prove or reject those axioms appeared important to

supporters of TC (there were some mathematicians among them) and to the

opponents.

There were some experiments that produced interesting results, such as

“Great Rabbis” experiment and others. Some saw in this a proof to the

“divinity” of Torah, which some people tried to show statistically. However

their approach and methods were rightly criticized, as a research was

sometimes inaccurate, besides allegedly similar results were obtained in

analyzing of other books such as the “War and Peace” by Tolstoy.

The “Great Mathematicians” experiment (GM)

The GM experiment took place before 1990.

The group of mathematicians, supporters or opponents of TC theory,

approached prof. N, authority in the field of probability and statistics, asking

him to define scientific experiment that will prove correctness (Heavenly

origin of Torah) of TC or prove the contrary. Prof.N had suggested the

following experiment: he listed twenty names of famous mathematicians,

asking to find in Torah (with the aid of TC, and I believe the computer

program calculating Torah Codes with different steps and differences was

needed for this end) the names of at least 18 from the list with addition of

words: “great mathematician” (‘X’ is a great mathematician, ’Y’ is a great

mathematician’ etc., in Hebrew:

שם‘מתמטיקאי גדול ‟). After searching the Torah with all possible steps, there

were found 17 names from the list and the 18-th was found in the form: ‘Z’ is

a genial mathematician! (In Hebrew: שם‘מתמטיקאי גאון ‟)

Everybody becomes merry and begins to laugh upon hearing this. Some,

perhaps, were happy because the experiment obviously succeeded, and also

showed, as if intentionally, by choosing other words for the 18th

mathematician, that it is as a living intelligent challenger. Obviously, the

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Torah is divine and also is laughing at those who made an experiment. I

laughed too, but perhaps had other reasons. I myself was discouraged from

seeking Torah Codes for long. But why it really seems, that Torah is joking?

The experiment succeeded. But it had, additionally, an unexpected end. It

seems that the experimenters should have thought about such linguistics

nuance, as finding instead of a “great mathematician” a synonym. But it was

not explicitly said, as I remember it, though perhaps was meant. It is perhaps

even question of “halacha”, the topic of the tractate “Nazir”36 about the use

of language, in this case, whether we should consider every expression with

the same meaning acceptable. Otherwise, from the point of view of statistics,

it seems that the experiment failed.

Furthermore, what if we will find not exactly synonyms, or even antonyms of

what we look for? How we should interpret the results?

Why should Torah comply with our definition and give us the result? Perhaps,

we could discover that Torah does not consider some mathematicians exactly

genial.

Of course, we assume that the mentioned statistical test took the size of the

text and other its qualities into consideration. So, I suppose, the output

proves the divinity of Torah for the examiners. But perhaps not for all, as

some would design the test otherwise.

There are few points, which generally can constitute a problem:

36

In the begining of tractate „Nazir“ there is a discussion about linguistic expression in

which a person accepts a vow to be a „nazir“. In many cases not explicit expression still

constitutes a vow.

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1. Were we not looking for exact phrase we would probably find a lot of

related material in any sufficiently long text researched. According to the law

of great numbers, if we will wait very long, we will find any given sentence

with probability 1 (almost sure) when reading text typed par hazard by a

monkey.

Is it our will for confirming the uniqueness and possibly not-human origin of

Torah that gives us inspiration to interpret the result or are those results

really encoded?

2. If we are speaking of meaning then the purpose of the research also defines

it. Here, for example, we were not looking to find great mathematicians of the

times, our aim was to prove or disprove something about Torah itself.

3. Such statistical methods are clearly not applicable to text, where almost

anything has meaning: in Hebrew almost half of combinations of any two

letter is a word, almost any root has no more than 3 letters, as vowels are

omitted and we are free to interpret the rest.

The general problem in applying mathematical methods to text is however

the right way of using it.

4. Originally, the meaningful discoveries by applying steps and arithmetic

progressions were made manually. The full research is impossible, obviously

in this way. However, using a computer program instead of the manual

method of searching for meaning makes TC not exactly codes in Torah, but

more of an Artificial intelligence program, which is Torah-based.

Perhaps it is impossible then to prove heavenly origin of Torah, based on TC,

nor to disprove it. Perhaps it is self-referencing in a way, so logically

problematic. It reminds us some paradoxes of Set theory and ambiguity

language. Here we will give two examples of such paradoxes, which the

reader can find in internet. (Wikipedia.)

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Grelling Paradox: Grelling-Nelson paradox37 iii

Conclusions - methodological:

We must formulate more appropriate methods for dealing with natural

languages, perhaps to translate the problem and the proof to formal

languages of logic.

As to allege similar results in research of “War and Peace” – so what?

Great works of human mind such as of Tolstoy or Bach or Escher can be also

heavenly inspired.

Why not be satisfied with just observing the Torah Codes? (not try to

prove anything and not to come to conclusion and predictions)

Divinity – what it employs?

Assuming, we have a mathematical prove of Torah’ divinity, we may ask

ourselves: what does it employ?

Some people will try to find explanation and (additional, not directly written)

treatment of things in Torah Codes, some will try to predict the future, or ask

for a sign before taking important decisions. While anybody with appropriate

software can do Torah Codes, is it legitimate or appropriate to use it in such a

way? Does it not remind us of some kind of witchcraft and sorcery?

Firstly, in ancient times, people were using this kind of method, when a man

was turning to a passing by child (usually – student in Beit-Midrash – religious

school) and asking him “פסוק לי פסוקיך” – say a verse from the Scriptures for

me!

37

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Then the man was interpreting the verse from Scriptures the child picked for

him (from head) as answering to his question. 38

We can examine Talmudic sources concerning the “asking for a sign.” The

passage in Talmud תלמוד(”, )"ארבע שאלו states “Four has asked in

inappropriate way, three of those were answered in appropriate way, and

one was answered in inappropriate way”. One of them was Eliezer, servant of

Abraham, when he was asking for a sign for right choice of the bride for

Isaac,39 who has asked in inappropriate way, because the girl could be an old,

38 “From the times the Temple was destroyed, the prophecy passed to imbeciles and the

children”

39(Genesis) 24,10 And the servant took ten camels, of the camels of his master, and

departed; having all goodly things of his master's in his hand; and he arose, and went to

Aram-naharaim, unto the city of Nahor. 24,11 And he made the camels to kneel down

without the city by the well of water at the time of evening, the time that women go out to

draw water. 24,12 And he said: 'O LORD, the God of my master Abraham, send me, I pray

Thee, good speed this day, and show kindness unto my master Abraham. 24,13 Behold, I

stand by the fountain of water; and the daughters of the men of the city come out to draw

water. 24,14 So let it come to pass, that the damsel to whom I shall say: Let down thy

pitcher, I pray thee, that I may drink; and she shall say: Drink, and I will give thy camels drink

also; let the same be she that Thou hast appointed for Thy servant, even for Isaac; and

thereby shall I know that Thou hast shown kindness unto my master.' 24,15 And it came to

pass, before he had done speaking, that, behold, Rebekah came out, who was born to

Bethuel the son of Milcah, the wife of Nahor, Abraham's brother, with her pitcher upon her

shoulder. 24,16 And the damsel was very fair to look upon, a virgin, neither had any man

known her; and she went down to the fountain, and filled her pitcher, and came up. 24,17

And the servant ran to meet her, and said: 'Give me to drink, I pray thee, a little water of thy

pitcher.' 24,18 And she said: 'Drink, my lord'; and she hastened, and let down her pitcher

upon her hand, and gave him drink. 24,19 And when she had done giving him drink, she said:

'I will draw for thy camels also, until they have done drinking.' 24,20 And she hastened, and

emptied her pitcher into the trough, and ran again unto the well to draw, and drew for all his

camels. 24,21 And the man looked stedfastly on her; holding his peace, to know whether the

LORD had made his journey prosperous or not. 24,22 And it came to pass, as the camels had

done drinking, that the man took a golden ring of half a shekel weight, and two bracelets for

her hands of ten shekels weight of gold; 24,23 and said: 'Whose daughter art thou? tell me, I

pray thee. Is there room in thy father's house for us to lodge in?' 24,24 And she said unto

him: 'I am the daughter of Bethuel the son of Milcah, whom she bore unto Nahor.' 24,25 She

said moreover unto him: 'We have both straw and provender enough, and room to lodge in.'

24,26 And the man bowed his head, and prostrated himself before the LORD. 24,27 And he

said: 'Blessed be the LORD, the God of my master Abraham, who hath not forsaken His

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ugly or otherwise inappropriate wife for Isaac. But God had answered (his

prayer) in appropriate way. From other hand Jephtah40 has asked in

inappropriate way – (Talmud: the living being who came to meet him could be

inappropriate for sacrificing, like any unclean animal –dog, horse, etc.) – and

was answered accordingly. So, just perhaps pay attention to your wording!

mercy and His truth toward my master; as for me, the LORD hath led me in the way to the

house of my master's brethren.'

40 Judges : 11,30 And Jephthah vowed a vow unto the LORD, and said: 'If Thou wilt indeed

deliver the children of Ammon into my hand, 11,31 then it shall be, that whatsoever cometh

forth of the doors of my house to meet me, when I return in peace from the children of

Ammon, it shall be the LORD'S, and I will offer it up for a burnt-offering.' {P}

11,32 So Jephthah passed over unto the children of Ammon to fight against them; and the

LORD delivered them into his hand. 11,33 And he smote them from Aroer until thou come to

Minnith, even twenty cities, and unto Abel-cheramim, with a very great slaughter. So the

children of Ammon were subdued before the children of Israel. {P}

11,34 And Jephthah came to Mizpah unto his house, and, behold, his daughter came out to

meet him with timbrels and with dances; and she was his only child; beside her he had

neither son nor daughter. 11,35 And it came to pass, when he saw her, that he rent his

clothes, and said: 'Alas, my daughter! thou hast brought me very low, and thou art become

my troubler; for I have opened my mouth unto the LORD, and I cannot go back.' 11,36 And

she said unto him: 'My father, thou hast opened thy mouth unto the LORD; do unto me

according to that which hath proceeded out of thy mouth; forasmuch as the LORD hath

taken vengeance for thee of thine enemies, even of the children of Ammon.' 11,37 And she

said unto her father: 'Let this thing be done for me: let me alone two months, that I may

depart and go down upon the mountains, and bewail my virginity, I and my companions.'

11,38 And he said: 'Go.' And he sent her away for two months; and she departed, she and

her companions, and bewailed her virginity upon the mountains. 11,39 And it came to pass

at the end of two months, that she returned unto her father, who did with her according to

his vow which he had vowed; and she had not known man. And it was a custom in Israel,

11,40 that the daughters of Israel went yearly to lament the daughter of Jephthah the

Gileadite four days in a year. {P}

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Predictability

From here we arrive to the problem of predictability. Are there certain

predictable events? It seems that it would contradict the free choice. Consider

situation, date of your death or other important event for you, is written in

Torah, so not only you know it, but also others! From other side, banks,

meteorological services, and almost every other service rely on it and spend

lots of money while researching the future. So the difficulty lies only in finding

the predictable future in the Torah itself, which is divine and absolute,

especially when our sages, specifically Maimonides, taught strongly against

that. Though there is infinitely many events (we percept the future in this

way, though, of course, according to modern physics, there will be end to the

Earth in normal sense), there are not infinitely many letter-combinations with

specific length in Torah: though there will be many different phrases (say, of

maximum 30 letters) if we allow “equal-length jumping”, there still will be

finite. iv

Linguistic difficulty

It is an old thing that everybody heard about, that there is some encoding in

Torah, that all the Torah is names of the God. However, it is difficult to accept

that Torah is encoded this way. In next parts I propose a much more likely

encryption method of Torah. Perhaps it will bring us some results.

ibliography for the TC appendixB

[1] Feller “Probability theory”

[2] Statement by 55 mathematicians

http://math.caltech.edu/code/petition.html

http://www.math.washington.edu/~greenber/BibleCode.html

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Appendix 2: Linguistics-mathematical paradoxes

Grelling Paradox: Grelling-Nelson paradox (see Wikipedia)

The Grelling-Nelson paradox can be taken as a demonstration that natural

language does not necessarily partition all objects of thought into well-

defined categories that will stand up to arbitrary logical scrutiny. And a word

is not itself the same as what it refers to.

The second paradox can be formulated as follows:

The number of all natural numbers is infinite. The set of all English sentences

consisting of no more than 20 words is finite. (If a dictionary consists of

100000 words, set of phrases of no more than 20 words has 100000 power 20

members, which is large, but finite). Let’s try to correspond each natural

number to a sentence from this set, so numbers will be defined by

corresponding English sentence of no more than 20 words. As the number of

all natural numbers is infinite, there will be some numbers without

corresponding sentence. Let’s take the first such number – the smallest one

which has not corresponding English sentence. But the sentence: “the

smallest natural number which cannot be defined by English sentence with no

more than 20 words” has only 17 words, is English and completely defines

that number! This is a contradiction.

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Blue&White publishing 2010 Copyright© Osnat Belaga – Youssin

iii

iv Let’s X be number of letters in Torah (or just Genesis) and N – length of phrase.

So, even if we allow to continue from the beginning of Torah, (when we did not yet count N

letters in specific jump, but already arrived to the end)

There will be maximum X*X different phrases.